West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 14% grade, which means th

Question

West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 14% grade, which means that its slope is − 14 100 . Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance in miles

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MichaelMet 6 months 2021-08-18T17:32:40+00:00 1 Answers 4 views 0

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    2021-08-18T17:34:35+00:00

    Answer:

    1.35 miles

    Explanation:

    Since the slope is 14% grade = -14/100. This is a negative slope.

    The distance of 1000 ft descended is a vertical descent, so assuming our initial position is 0, and Δx is the change in horizontal distance.

    tanθ = -14/100 = (0 – 1000)/Δx = – 1000)/Δx

    -14/100 = – 1000)/Δx

    Δx = -1000 × -100/14= 7142.86 ft

    5280 ft = 1 mile

    7142.86 ft = 7142.86/5280 miles = 1.353 miles ≅ 1.35 miles

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